where \(m\)  is the Riemannian volume. Among the most significant physical measures are the Sinai-Ruelle-Bowen (SRB) measures. These are invariant measures for hyperbolic dynamical systems that have conditional measures on unstable leaves that are absolutely continuous with respect to the Riemannian leaf volume. For uniformly hyperbolic dynamical systems (such as transitive Anosov diffeomorphisms and attractors of Axiom A systems), there is a unique SRB measure [1]}, and the existence of SRB measures has been established for several classes of nonuniformly hyperbolic dynamical systems [2]}, [3]}, [4]} and partially hyperbolic dynamical systems [5]}, [6]}. It was further shown in [7]} that if \(M\)  is a compact Riemannian 2-manifold and \(f : M \rightarrow M\)  is a hyperbolic diffeomorphism admitting an SRB measure, then this SRB measure is unique.
